Finnegan left Monday's game in the fourth inning with a left triceps strain.
This is a tough blow for Finnegan, as Monday marked his first start since April 15 after spending more than two months on the DL with a shoulder strain. The Reds haven't yet provided a timetable for the 24-year-old, though it should become clearer after he's further evaluated Tuesday. A trip back to the disabled list seems possible at this point, in which case lefty-throwing Amir Garrett would be an option to return from Triple-A Louisville to take his place in the rotation. Finnegan has made just four starts this season, lasting a combined 13 innings.